

REVIEW ARTICLE 

Year : 2014  Volume
: 3
 Issue : 2  Page : 8588 

Finite element analysis: New dimension in prosthodontic research
Swapnil Ramchandra Chopade, Venigalla Naga Venu Madhav, Jayant Palaskar
Department of Prosthodontics and Crown and Bridge, Sinhgad Dental College and Hospital, Pune, Maharashtra, India
Date of Web Publication  18Jun2015 
Correspondence Address: Dr. Swapnil Ramchandra Chopade "Trimutri" Plot No. 7, Vivekanand Housing Society, In Front of Bharat Soot Girni, Sangli  416 416, Maharashtra India
Source of Support: None, Conflict of Interest: None  Check 
DOI: 10.4103/22774696.159089
Finite element analysis method (FEA) allows detailed visualization of where structures bend or twist, and indicates the distribution of stresses and displacements. FEA software provides a wide range of simulation options for controlling the complexity of both modeling and analysis of a system. Similarly, the desired level of accuracy required and associated computational time requirements can be managed simultaneously to address most engineering applications. FEA which is an engineering method of calculating stresses and strains in all materials including living tissues has made it possible to adequately model the tooth, restorative materials and dental implants for scientific checking, and validating the clinical assumptions. The purpose of this article was to give an insight of the FEA, which has totally overshadowed other experimental analysis due to its ability to model even the most complex of geometries with is immensely flexible and adaptable nature. FEA is a computerbased numerical technique for calculating the strength and behavior of structures. Keywords: Element method, finite element analysis, stress analysis
How to cite this article: Chopade SR, Madhav VV, Palaskar J. Finite element analysis: New dimension in prosthodontic research. J Dent Allied Sci 2014;3:858 
How to cite this URL: Chopade SR, Madhav VV, Palaskar J. Finite element analysis: New dimension in prosthodontic research. J Dent Allied Sci [serial online] 2014 [cited 2020 Jan 25];3:858. Available from: http://www.jdas.in/text.asp?2014/3/2/85/159089 
Introduction   
Several methodologies have been developed with the aim of improving our understanding of the distribution of forces in the stomatognathic system. Among such methodologies, it is possible to mention photoelastic models, analytical mathematical models, use of strain gauges, and analyses such as the finite element analysis (FEA). ^{[1]} Photoelasticity provides good qualitative information pertaining to the overall location of stresses but only limited quantitative information. Strain gauge measurements provide accurate data regarding strains only at the specific location of the gauge. FEA is capable of providing detailed quantitative data at any location within the mathematical model. Thus, FEA has become a valuable analytical tool in dentistry. A more recent method of stress analysis, generally developed in 1956 in the aircraft industry was the FEA. This technique was used widely only in aerospace engineering at first but slowly due to the flexibility of the method to model any complex geometries and provide instant results, it made its presence felt in dentistry in early 1970's. ^{[2]}
What is Finite Element Analysis?   
"Finite element analysis," because a region could be only broken up into a finite number of elements, and because many of the ideas were extrapolated from an infinitesimal element of the theory to a finite sized element of practical dimensions. ^{[3]} In FEA, the behavior of a particular physical system is mathematically simulated. A continuous structure is divided into different elements, which maintain the properties of the original structure. Each of these elements is described by differential equations and solved using mathematical models selected according to the data under investigation. ^{[4],[5],[6],[7]} FEA allows creating models for complex structures, reproducing the irregular geometries of either natural or artificial tissues. In addition, FEA allows to modify the parameters of those geometries, which makes it possible to apply a force or a system of forces to any point and/or in any direction, thereby providing information on movement and on the degree of tension and compression forces caused by these loads. ^{[8],[9],[10]}
The use of numerical methods such as FEA has been adopted in solving complicated geometric problems, for which it is very difficult to achieve an analytical solution. ^{[11]} FEA is a technique for obtaining a solution to a complex mechanics problem by dividing the problem domain into a collection of much smaller and simpler domains (elements) where field variables can be interpolated using shape functions. An overall approximated solution to the original problem is determined based on variational principles. In other words, FEA is a method whereby, instead of seeking a solution function for the entire domain, it formulates solution functions for each finite element and combines them properly to obtain a solution to the whole body. A mesh is needed in FEA to divide the whole domain into small elements. The process of creating the mesh, elements, their respective nodes, and defining boundary conditions is termed "discretization" of the problem domain. ^{[11]}
Finite analysis solves a complex problem by redefining it as the summation of the solution by a series of interrelated simpler problems. The first step is to subdivide (i.e., discretize) the complex geometry into a suitable set of smaller "elements" of "finite" dimensions when combined with the "mesh" model of the investigated structures. Each element can adapt a specific geometric shape (i.e., triangle, square, tetrahedron etc.) with a specific internal strain function. Using these functions and the actual geometry of the element, the equilibrium equations between the external forces acting on the element and the displacements occurring on its nodes can be determined. Information required for the software used in the computer is as follows:
 Coordinates the nodal points.
 Number of nodes for each element.
 Young's modulus and Poisson's ratio of the material modeled by different elements. ^{[1]}
 The initial and boundary conditions.
 External forces applied on the structure.
 The boundary condition of these models is defined so that all the movements at the base of the model are restrained. This manner of restraining prevents the model from any rigid body motion while the load is acting.
Advantages and disadvantages of finite element analysis
The advantages of FEA, some already touched upon, may be summarized as follows: ^{[12]}
 Any domain with curved boundaries, heterogeneous material properties, irregular support constraints, and varying loading conditions, may be subdivided into a suitable number of finite elements, appropriate material, and behavior properties may be ascribed to them, and the resulting governing equations may be solved quickly and accurately by computers.
 It is equally applicable to statics and dynamics; solids, fluids, and gases and combinations; linear and nonlinear; elastic, inelastic or plastic; special effects such as crack propagation; events and processes like bolt pretensioning, etc.
 The massive amounts of data itself can be efficiently generated by computer "preprocessors," and the even more voluminous output can be effectively analyzed and presented by "postprocessors." Hence, a larger problem does not involve undue additional effort for users.
 Problems of size and complexity hitherto unimaginable and infeasible can be handled by FEA, enabling analysts to extend their investigations into fresh areas and inspiring designers to create new forms and new solutions.
 Where formerly only a few alternatives could be examined, with FEA quite a large number of possible solutions could be tested, resulting in optimal solutions.
However, certain disadvantages and limitations of FEA should also be recognized: ^{[12]}
 Every finite element is based on an assumed shape function expressing internal displacements as functions of nodal displacements. A certain element may give accurate answers for a particular type and location of support and loading, but inaccurate answers for another type and location.
 Even with "wellbehaved" elements, the solution is heavily dependent on the mesh, not only on the number of elements into which the region is divided, but also on their shape and arrangement.
Methodology   
Development of the geometric model
The first step before an FEA model can be obtained is the creation of a virtual geometry model (VGM). The VGM will serve as the basis for the subsequent creation of the FEA, and, therefore, any errors at this stage may render the model and the study results irrelevant. The type of VGM created (two or threedimensional [2D or 3D]) should be determined depending on the characteristics and analyses that the investigator intends to perform. 2D models are simpler, but allow anteroposterior assessments only. ^{[13],[14],[15]} 3D models, in turn, are more complex but allow a more complete assessment of structures and loads, in any direction. ^{[10],[16],[17]} VGMs can also be described in terms of their precision, that is, models that more closely resemble the real structures will produce more reliable results.
The attractive feature of the finite element is the close physical resemblance between the actual structure and its finite element model. Excessive simplifications in geometry will inevitably result in considerable inaccuracy. The model is not simply an abstraction; therefore, experience and good engineering judgment are needed to define a good model. Whether to perform a 2D or 3D finite element model for the study is a significant query in FEA. It is usually suggested that when comparing the qualitative results of one case with respect to another, a 2D model is efficient and just as accurate as a 3D model; although the time needed to create finite element models is decreasing with advanced computer technology, there is still a justified time and cost savings when using a 2D model over 3D, when appropriated. However, 2D models cannot simulate the 3D complexity within structures, and, as a result, are of little clinical values. The group of 3D regional FE models is by far the largest category of mandible related researches. This is because modeling only the selected segment of the mandible is much easier than modeling the complete mandible. In many of these regional models, reproduced boundary conditions are often oversimplified and yield too much significance to their predictive, quantitative outcome.
Mesh generation
Once the VGM has been obtained, it should be processed by another software in order to generate the finite element mesh, several software options are currently available and can be used for FEA mesh generation, with satisfactory results, particularly Ansys (Swanson Analysis Systems, Houston, PA, USA) and MSC/Nastran (MSC Software Corporation, Santa Ana, CA, USA). These options have different interfaces and characteristics, and all are capable of generating the desired mesh and subsequently performing preestablished analyses. The finite element mesh comprises spatial coordinates represented by quadrilateral elements combined and arranged to produce different geometric shapes  triangles, tetrahedrons, and hexahedrons (most commonly the latter two). The higher the number of quadrilaterals used to generate the mesh, the higher the precision and reliability of FEA in relation to the VGM. The quadrilaterals used in mesh generation are connected by nodes, resulting in a complex 2D or 3D net, which allows the transport of mathematical equations between the coordinates.
Behavior and Properties of Physical Models   
In general, material behavior can be classified into five categories: Nonlinear elastic phenomena (return to original conditions after deformation, not following a specific pattern), plastic phenomena (deformation without return to original conditions), elastoplastic phenomena (partly elastic and partly plastic behavior), viscoelastic phenomena (return to original conditions after deformation is timedependent), and viscoplastic phenomena (timedependent deformation without return to original conditions).
Material properties greatly influence the stress and strain distribution in a structure. These properties can be modeled in FEA as isotropic, transversely isotropic, orthotropic, and anisotropic. In most reported studies, an assumption was made that the materials were homogenous and linearly isotropic. This classification is based on the mechanical properties of a material in relation to the directions of each of the axes (X, Y, and Z): Isotropic materials are defined as those that present the same properties in every direction; in anisotropic materials, properties are different along the directions; finally, in orthotropic materials, properties are the same in two directions and different in the third.
The last factors to be considered and included in the generated mesh are Poisson's ratio, Young's modulus, and information on the density of each material. Each of these factors will provide the software with data on how a given material behaves when submitted to force application taking into consideration its deformation capacity, elasticity, and behavior under tension or compression.
Boundary Conditions   
Zero displacement constraints must be placed on some boundaries of the model to ensure an equilibrium solution. The constraints should be placed on nodes that are far away from the region of interest to prevent the stress or strain fields associated with reaction forces from overlapping with each other.
Analysis and Evaluation of Results   
Once force and time properties have been properly defined, the software performs a series of calculations and mathematical equations and yields the simulation results. These are presented according to a color scale where each shade represents a different degree of movement, tension, or compression. The model also allows selecting one particular axis or structure for the analysis of tension/compression or movement, allowing simulation of a variety of events and thereby increasing the possibilities of analysis.
Application of finite element analysis in dentistry
 Plastic and viscoelastic behaviors in materials: ^{[10]} FEA has been used in studies to evaluate various materials used in dentistry to know their behavior under load and stress.
 Toothtotooth contact analysis: ^{[10]} Sliding and friction phenomena critically affect the stress and strain created on the contact surfaces between teeth.
 Contact analysis in implant structures: ^{[10]} FEA has been used in understanding the designing and behavior of implants and stress analysis of implants, abutments and the stress within the bone.
 FEA has been used in orthodontics to study growth and development.
 Interfacial stress in restorations: ^{[10]} FEA has been of value in understanding the design of dental restorations.
 To investigate stress distribution during cavity preparation and root canal treatment in endodontics.
 To study stress distribution on supporting structures in relation during designing of fixed and removable prostheses.
 Nonlinear simulation of periodontal ligament property: ^{[10]} It has been used to analyze stresses produced in the periodontal ligament under different loading conditions and with
 varying amounts of bone levels.
Conclusion   
With rapid improvements and developments of computer technology, the FEA has become a powerful technique in dental implant biomechanics because of its versatility in calculating stress distributions within complex structures. By understanding the basic theory, method, application, and limitations of FEA in implant dentistry, the clinician will be better equipped to interpret results of FEA studies and extrapolate these results to clinical situations. Thus, it is a helpful tool to evaluate the influence of model parameter variations once a basic model is correctly defined. Further research should focus on analyzing stress distributions under dynamic loading conditions of mastication, which would better mimic the actual clinical situation.
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